Russian Mathematics Education: Programs and Practices

Contents......Page 6
Introduction......Page 8
1 Introduction......Page 10
2.1 Teachers and Students......Page 12
2.2 The Mathematics Classroom and Its Layout......Page 15
3.1 On the History of the Development of Class Instruction Methodology in Russia......Page 19
3.2 Types of Lessons and Lesson Planning......Page 26
4 Problem Solving in Mathematics Classes......Page 29
5 Epilogue: Bad Lessons, and What One Would Like to Hope for......Page 40
References......Page 44
2 The History of Arithmetical Education in Russia During the 10th–18th Centuries......Page 46
3 Elementary Mathematical Education in Russia in the 19th and Early 20th Centuries (through 1917)......Page 50
3.1 The Method of Learning Operations......Page 51
3.2 The Monographical Method of Learning the Numbers......Page 52
3.3 On Some Pre-Revolution Handbooks for the Elementary School......Page 53
4 Elementary Education in the Complex Programs of Soviet Russia, 1918–1932......Page 59
5 The Study of Arithmetic in the Soviet Elementary School, 1932–1969......Page 62
6 The Elementary Course in Mathematics in the Soviet School, 1969–1990s......Page 64
7.1 Fundamental Program Requirements and Characteristics of Contemporary Textbooks......Page 69
7.2.1 Numbers and arithmetical operations......Page 75
7.2.2 Arithmetical problems......Page 79
7.2.3 Magnitudes......Page 80
7.2.4 Geometrical content......Page 81
7.2.5 Elements of algebra......Page 82
7.2.6 Elements of combinatorics......Page 83
7.2.8 Working with data......Page 84
References......Page 86
1 Introduction......Page 90
2 The Contents of the Course in Geometry in Russian Schools......Page 91
3 The Aims and Characteristics of the Course in Geometry in Russia......Page 94
4 On the Conditions Under Which Geometry Is Taught......Page 100
5.1 From Kiselev to Kolmogorov......Page 104
5.2 Kolmogorov’s Textbooks for Basic Schools......Page 108
5.3 Geometry Textbooks for Basic Schools from the Late 1970s to the 1980s......Page 112
5.3.1 A. V. Pogorelov’s geometry textbook......Page 114
5.3.2 The geometry textbooks of L. S. Atanasyan and his coauthors......Page 116
5.3.3 The textbooks of A. D. Alexandrov and his coauthors......Page 118
5.4 Textbooks That Appeared After the Collapse of the USSR......Page 121
5.4.1 I. F. Sharygin’s textbooks......Page 122
5.4.2 The textbooks of I. M. Smirnova and V. A. Smirnov......Page 124
5.4.3 The textbooks of A. L. Werner and his coauthors......Page 125
6.1 The Problem of the Rigor of the Course in Geometry......Page 127
6.2 Visual and Informal Geometry in the Study of Three-dimensional Geometry in Basic Schools......Page 130
6.3 The New and the Old in the Teaching of Geometry......Page 131
References......Page 134
1 Algebra as a School Subject......Page 138
2 The Algebraic Component in the System of School Mathematics Education......Page 139
3 The Content of Algebra Education in Russian Schools......Page 140
4.1.1 An Overview......Page 147
4.1.2 Algebra for students of ages 10–12 (grades 5–6)......Page 149
4.1.3 Algebra for students of ages 12–15 (grades 7–9)......Page 158
4.1.4 Examples of test problems......Page 174
4.2.1 An overview......Page 181
4.2.2 The study of algebraic expressions in grades 10–11......Page 184
4.2.3 Equations and inequalities in the basic and advanced courses in mathematics in grades 10–11......Page 193
4.2.4 The final attestation in algebra for 11th graders......Page 195
References......Page 196
1 Introduction......Page 200
2 Elements of Analysis in Normative Documents......Page 202
3.1 The Second Third of the 18th Century to 1845......Page 204
3.3 1907–1917......Page 205
3.4 1918–1933......Page 206
3.6 1965–1976......Page 207
3.7 1977 to the End of the 1980s......Page 208
4 Introduction to Analysis: Functions in Basic School......Page 209
5 Algebra and Elementary Calculus: Functions in Grades 10–11......Page 217
6 Elements of Differential and Integral Calculus......Page 222
6.1 Andrey Kolmogorov’s Textbook......Page 223
6.2 The Textbooks of Alimov et al. and Kolyagin et al.......Page 228
6.3 M. I. Bashmakov’s Textbook......Page 230
6.4.1 The textbook of A. G. Mordkovich and I. M. Smirnova......Page 232
6.4.2 The textbook of G. K. Muravin and O. V. Muravina......Page 233
7 Conclusion......Page 234
References......Page 236
1 Finite Mathematics in the School Curriculum Prior to the Revolution of 1917......Page 240
2 Finite Mathematics in the Secondary School Curriculum in the Soviet Period......Page 243
3 Finite Mathematics in the Post-Soviet Period......Page 249
4 Features of Contemporary Approaches to the Study of Finite Mathematics in Russian Schools......Page 256
5 First Results of Teaching the Experimental Curriculum......Page 262
References......Page 268
1 Introduction......Page 274
2 The Appearance of Schools and Classes with an Advanced Course in Mathematics......Page 276
3 Mathematics Schools During the Period of Stagnation and Later......Page 283
4 The Everyday Life of Mathematics Schools......Page 290
5.1 On Curricula......Page 297
5.2 On the Specifics of Teaching the Course in Mathematics......Page 300
5.3 On the Content of Certain Topics in the Course......Page 303
5.4 On Textbooks for Schools with an Advanced Course of Study in Mathematics......Page 309
6 Schools with a Humanities Orientation......Page 313
7 Curricula and Textbooks for Humanities-Oriented Schools......Page 317
8 Conclusion......Page 322
References......Page 323
1 Introduction......Page 328
2.1 What Is Assessed and Why?......Page 330
2.2 Assessment in the Past......Page 332
2.3 Some Facts About the Organization of the Teaching Process and of Assessment......Page 334
3 On the Nature of the Assignments Used for Assessment......Page 338
4 Oral Questioning in Class......Page 346
4.1 The “From the Seat” Response......Page 347
4.2 The “At the Board” Response......Page 349
4.2.1 Going over homework assignments......Page 350
4.2.2 Questioning students about theoretical material......Page 351
4.2.3 Solving problems on the blackboard......Page 352
5.1 Tests......Page 354
5.2 Quizzes......Page 359
5.3 Mathematical Dictations......Page 362
5.4 Individual Written Questioning of the Student in Class......Page 363
6 Long-Term Assignments......Page 365
7.1 Oral Survey Tests......Page 367
7.2 Exams......Page 371
8 Conclusion......Page 378
References......Page 379
1 Introduction......Page 384
2 Mass Forms of Extracurricular School Work......Page 386
2.1 Mathematical Wall Newspapers......Page 387
2.2 Mathematical Theatrical Evenings and Oral Mathematics Journals......Page 388
2.3 Mathematical Tournaments......Page 389
2.4 Written Problem-Solving Contests......Page 391
3 School Mathematics Circles and Electives......Page 392
3.1 Mathematics Circles in Grades 5–6......Page 395
3.2 Mathematics Circles and Electives in Grades 7–9......Page 396
3.3 Mathematics Circles and Electives in Grades 10–11......Page 400
4 On Various Forms of Distance Learning......Page 402
5 Selective Forms of Working with Students......Page 406
5.1 On Mathematics Circles......Page 408
5.2 Mathematics Summer Camps......Page 412
5.3 Conferences......Page 413
6 Conclusion......Page 415
References......Page 416
1 Introduction......Page 420
2 On Certain Features of the Organization of Scienti.c Research in the Area of Mathematics Education and on Our Sources......Page 421
3 Issues in the Philosophy and Worldview of Mathematics Education......Page 426
4 The Psychology of Mathematics Education......Page 428
5 Problem Solving......Page 431
6 The History of Mathematics Education......Page 433
7 Issues of Differentiation in Education......Page 438
8 The Organization of the Educational Process......Page 440
9 Studying the Process of Teaching Mathematics: Connections Within Subjects, Continuity and Succession in Education......Page 443
10 Teaching Aids......Page 447
11 Teaching in Elementary Schools......Page 449
12 On Teaching Speci.c Mathematical Subjects in Schools......Page 453
13 Teaching in Nonpedagogical Institutions of Higher Education......Page 457
14 Mathematics Teacher Education......Page 460
14.1 General Questions of Mathematics Teacher Education......Page 461
14.2 Special Aspects of the Methodological Preparation of Future Teachers......Page 465
14.3 On Teaching Mathematics to Future Teachers......Page 470
14.4 Technology in Mathematics Teacher Education......Page 474
15 On Candidate’s Dissertations......Page 475
16 Conclusion......Page 477
References......Page 480
Notes on Contributors......Page 496
Name Index......Page 502
Subject Index......Page 510